Part 4/6:
For ( a = 1/2 ): This function represents the square root, appearing as a curve defined only for non-negative values of ( x ).
For ( a = 1/3 ): It yields a curve reflective of the cube root function, illustrating similar behavior but with distinct symmetry properties.
These root functions highlight the transformation of their standard power forms, depicted mainly in the northern quadrant of the graph for even roots ( (y = x^{1/2}) ) while retaining some odd symmetry for odd roots ( (y = x^{1/3}) ).
Case 3: Negative Exponents
Reciprocal Functions
The final case involves negative powers, showcasing reciprocal functions, where ( a = -1 ).